Partial Differential and Integral Equations

This volume of the Proceedings of the congress ISAAC '97 collects the con­ tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal­ ysis are studied which are applied to the time-harmonic Maxwell equations.

Table of Contents:
1 Gauss-Manin Connexion of Curve Singularities.- 2 Group Convolution Operators on Step of Two Nilpotent Lie Groups.- 3 Some Boundary Value Problems for Second Order Overdetermined Elliptic Systems in the Unit Ball of ?n.- 4 Riemann-Hilbert Boundary Value Problems in ?n.- 5 The Riemann-Hilbert Problem for Nonlinear Elliptic Complex Equations of First Order in Multiply Connected Infinite Domains.- 6 The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type.- 7 On Totally Real Non-Compact Manifolds Globally Foliated by Analytic Discs.- 8 Boundary Behaviour of Vector-Valued Functions of Two Classes in Locally Convex Spaces.- 9 On Singular Integrals of the Time-Harmonic Maxwell Equations Theory.- 10 Systems of First Order Partial Differential Equations — a Hypercomplex Approach.- 11 To Elliptic Theory for Domains with Piecewise Smooth Boundary in the Plane.- 12 Boundary Value Problems for a System of First Order Equations of a Principal Type in the Plane.- 13 The Stabilityof the Riemann Boundary Value Problem for Vector-Valued M-Analytic Functions.- 14 A Class of Inverse Hilbert Boundary Value Problems.- 15 Cauchy Formula, Integral of Cauchy Type and Hilbert Problem for Bianalytic Functions.- 16 On Uniqueness Conditions for Entire Polyharmonic Functions.- 17 Bi-Analytic Functions and Their Applications in Elasticity.- 18 Effect of Periodic Gasket on a Periodic Contact Problem.- 19 Singular Integral Operators and Singular Quadrature Operators for Singular Integral Equations with Hilbert Kernel.- 20 Some Co-Circular Crack Problems with Cyclic Symmetry.- 21 The Oblique Derivative Problem for Nonlinear Parabolic Equations of Second Order with Measurable Coefficients in a Higher Dimensional Domain.- 22 Existence and Uniqueness for Boundary Value Contact Problems.- 23 Weakly Hyperbolic Equations — a Modern Field in the Theory of Hyperbolic Equations.- 24 Eigenvalue Problems for Elliptic Type Partial Differential Operators with Spectral Parameter Contained Linearly in Boundary Conditions.- 25 On Indefinite Nonlinear Neumann Problems.- 26 Higher Order Ordinary Differential Equations with Super-Singular Points.- 27 Applications of Methods of Integrals and Function Theory to Statistics.